How to use emitter for generating thick forest so that trees would not intersect?
I would suggest to disable Emit in Random order.



Particles in this case are emitted from faces. Every faces has it's own id. With the Random opton enabled you are asking Blender to pick a Random face id to generate the next particle.

In this case, where your simulation does'n run trought time, means that is very likely to have a particle create in the same place of another.

Let's say you have 100 faces. First random id is 1, so a tree is generated in Face1. Than pick another id, randomly..it may occour to pick the same id..1, so the generated tree will be overlapped to the previous one. It may seems that you have a low probability to pick the only 1% that is already came out, but you have to consider that for each particle cration iteration, the number of "free" ids lower, so when you are at half of the particle cration, you'll have 50% probability of overlap.

If this effect is not very strong is because you have also Random distribution option enabled.



With that, you are asking to position randomly the created tree on the face. So , despite they are created on the same face, the might have different location. On th other side, it may occour that two tree of born in adiacent faces, let's say along the common border, will be very near, causing overlap.

Particles generation is not aware of where other particles have previously been generated (it would be very high computing demanding for large numbers), so for now it is not possible to have a random distribution without any overlaps.



One possible workaround can bw to subdivide your mesh till the faces are almost the size of the trees XY bounding plane. Now you should have about 2000 faces in the "forest area". If we put without a tree in the center of each faces we would be able to create about 2000 trees without any overlap.



This obiuvsly resamble more to a plantation than a forest, but by lowering the amount of trees and the use of voronoi density map:



you should be able to dampen the "grid" effect a bit.